The SDI was the main avenue for upping the ante, so that naturally would've been the Soviets' primary concern at such conferences.
Which was the goal of Reagan and the CIA Director.
In terms of actual spending, the response to the SDI simply wasn't that big relative to the military budget.
It did add pressures to it. SDI wasn't huge, but it increased the military budget to more than they wanted. But they had to do it to keep up.
but PR concerns were kind of less important during the time Gorby was in power - when the politburo knew he wasn't very pliant, compared to perestroika, etc. doing practically nothing in terms of toning down American policies towards the Soviets.
Taking him out as soon as he was put in (basically) would have looked desperate. At least by 1991, it may have looked better.
Don't overlook the rhetoric either. Reagan's speech at Moscow State University had a profound effect on the youth of that country. It is one of the most important speeches in US history, IMO (and even Democrats will admit that

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